Quantum Chaos is the study of the quantum mechanics of classically chaotic systems. The field is currently a very active area of research. Our main thrust is to explore, via electromagnetic experiments, the manifestations of classical chaos in wave mechanics.

Our research program has led to several noteworthy observations listed below:

  • Experimental “proof” of a mathematical theorem on “Not Hearing the Shape of Drums”. Click here to see cover story in Science News.
  • Direct experimental observation of scars in quantum eigenfunctions of microwave cavities. Phys. Rev. Lett. , 67, 785 (1991)
  • Experimental observation of localized wavefunctions in disordered billiards, and deviations from the Porter-Thomas distribution due to localization in disordered billiards. These were the first experiments to be performed on disordered billiards. Phys. Rev. Lett., 75, 822 (1995)
  • First experimental observation of quantum fingerprints of classical Ruelle-Pollicott resonances. Phys. Rev. Lett., 85, 2360 (2000), Nobel Symposium on “Quantum Chaos Y2K”
  • Experimental studies of correlations of chaotic and disordered eigenfunctions and comparison with supersymmetry nonlinear sigma models. Phys. Rev. Lett., 85, 2360 (2000)
  • Tunneling Proximity Resonances: Experimental observation using dielectric resonators Phys. Lett. A, 268 (4-6), 399 (2000)
  • Precision tests of universal aspects of quantum spectra, observation of a “correlation hole”, and tests of applicability of Random Matrix Theories to microwave cavities. Phys. Rev. E. (Rapid Comm.), 49, R11 (1994)
  • Observation of Porter-Thomas distribution and fluctuations in eigenfunctions of chaotic billiards. Phys. Rev. Lett., 75, 822 (1995)
  • Observation of quantum resonances, universal properties, and comparison with semiclassical theories of the n-disk system. Phys. Rev. Lett., 82, 5233 (1999), Phys. Rev. E, 61, 3652 (2000)

It is evident that the experiments are able to explore a remarkable range of issues in Quantum Chaos, including tests of fundamental theories and different classical limits. The microwave experiments have yielded entirely new insights and perspectives concerning the quantum-classical correspondence. The reasons for this success are the ability to study well-defined geometries where the classical dynamics is clearly known, and the precision and flexibility of the experiments. The experiments have led to tests of key theoretical ideas while at the same time raising entirely new questions and motivating theorists in new directions.

Our work in this area is currently funded by National Science Foundation (Division of Atomic, Molecular and Optical Physics).

Related Posts

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Localization of Wavefunctions in Disordered Billiards

Experimental observation of localized wavefunctions in disordered billiards, and deviations from the Porter-Thomas distribution due to localization in disordered billiards. These were the first experiments to be performed on disordered billiards.

We show the evolution of localization with increasing scattering by measuring wavefunctions in disordered billiards.

Related Publications

Lu, WT; Zeng, Weiqiao; Sridhar, S
Duality between quantum and classical dynamics for integrable billiards Journal Article

(Abstract | Tags: Quantum Chaos)

Physical Review E, 73 (4), pp. 046201, 2006.
Lu, WT; Sridhar, S
Long range correlations among the eigenvalues of polygonal billiards and Riemann zeros Journal Article

(Abstract | Tags: Quantum Chaos)

APS, 2004 , pp. D19–004, 2004.
Lu, WT; Sridhar, S
Correlations among the Riemann zeros: Invariance, resurgence, prophecy and self-duality Journal Article

(Abstract | Tags: Quantum Chaos)

arXiv preprint nlin/0405058, 2004.
Lu, WT; Sokoloff, JB; Sridhar, S
Classical physics, including nonlinear media and photonic materials-Refraction of electromagnetic energy for wave packets incident on a negative-index medium is always negative Journal Article

(Tags: Quantum Chaos)

Physical Review-Section E-Statistical Nonlinear and Soft Matter Physics, 69 (2), pp. 26604–26604, 2004.
Wen-tao, Lu T; Sridhar, Srinivas; Zworski, Maciej
Fractal Weyl laws for chaotic open systems Journal Article

(Abstract | Tags: Quantum Chaos)

2003.
Pradhan, Prabhakar; Lu, Wentao T; Sridhar, S
Statistics of the Eigenfunctions of Chaotic and Disordered Quantum Systems: A Disordered Tight Binding Model Calculation Inproceedings

(Abstract | Tags: Quantum Chaos)

APS Meeting Abstracts, 2003.
Lu, WT; Sridhar, Srinivas; Zworski, Maciej
Fractal Weyl laws for chaotic open systems Journal Article

(Abstract | Tags: Quantum Chaos)

Physical review letters, 91 (15), pp. 154101, 2003.
Sato, Daisuke; Lu, Wentao; Pradhan, Prabhakar; Sridhar, Srinivas
Spectral statistics of microwave disordered billiards Inproceedings

(Abstract | Tags: Quantum Chaos)

APS Meeting Abstracts, 2003.
Dhar, Abhishek; Rao, Madhusudhana D; Sridhar, S; others,
Isospectrality in chaotic billiards Journal Article

(Abstract | Tags: Quantum Chaos)

Physical Review E, 68 (2), pp. 026208, 2003.
Sridhar, S; Lu, WT
Sinai billiards, Ruelle zeta-functions and Ruelle resonances: microwave experiments Journal Article

(Abstract | Tags: Quantum Chaos)

Journal of statistical physics, 108 (5-6), pp. 755–765, 2002.
Pradhan, Prabhakar; Sridhar, S
From chaos to disorder: Statistics of the eigenfunctions of microwave cavities Journal Article

(Abstract | Tags: Quantum Chaos)

Pramana, 58 (2), pp. 333–341, 2002.
Sridhar, S; Lu, WT
Sinai billiards, Ruelle zeta-functions and Ruelle resonances: microwave experiments. e-print Journal Article

(Abstract | Tags: Quantum Chaos)

2002.
Sinai, Ya G; Young, Lai-Sang; Sridhar, S; Lu, WT; van Beijeren, Henk; Dorfman, JR; Jakšic, V; Pillet, CA; Gallavotti, G; Lebowitz, JL; others,
Some Ill-Formulated Problems on Regular and Messy Behavior in Statis-tical Mechanics and Smooth Dynamics for Which I Would Like the Advice of Yasha Sinai David Ruelle What, in My Opinion, David Ruelle Should Do in the Coming Years Journal Article

(Tags: Quantum Chaos)

Journal of Statistical Physics, 108 (3/4), 2002.
Lu, WT; Sridhar, S; others,
Spectra and wave functions of open chaotic billiards Inproceedings

(Abstract | Tags: Quantum Chaos)

APS Division of Atomic, Molecular and Optical Physics Meeting Abstracts, 2002.
Sridhar, Srinivas
Quantum Chaos in Microwave Billiards Inproceedings

(Abstract | Tags: Quantum Chaos)

APS Division of Atomic, Molecular and Optical Physics Meeting Abstracts, 2002.
Lu, Wentao T; Prance, Kristi; Pradhan, Prabhakar; Sridhar, S
Quantum correlations and classical resonances in an open chaotic system Journal Article

(Abstract | Tags: Quantum Chaos)

Physica Scripta, 2001 (T90), pp. 238, 2001.
Sridhar, S
Quantum resonances and decay of a fractal repeller observed using microwaves Inproceedings

(Abstract | Tags: Quantum Chaos)

APS Meeting Abstracts, 2000.
Sridhar, S
Quantum chaos, localization and tunnelling: microwave experiments on model geometries Journal Article

(Abstract | Tags: Quantum Chaos)

Philosophical Magazine B, 80 (12), pp. 2129–2141, 2000.
Pance, Kristi; Lu, Wentao; Sridhar, S
Quantum fingerprints of classical ruelle-pollicott resonances Journal Article

(Abstract | Tags: Quantum Chaos)

Physical review letters, 85 (13), pp. 2737, 2000.
Pradhan, Prabhakar; Sridhar, S
Correlations due to localization in quantum eigenfunctions of disordered microwave cavities Journal Article

(Abstract | Tags: Quantum Chaos)

Physical review letters, 85 (11), pp. 2360, 2000.
Pradhan, Prabhakar; Pance, Kristi; Rose, Michael; Sridhar, S
From Localization to Chaos in experimental eigenfunctions of disordered microwave cavities Inproceedings

(Abstract | Tags: Quantum Chaos)

APS Meeting Abstracts, 2000.
Lu, Wentao; Viola, Lorenza; Pance, Kristi; Rose, Michael; Sridhar, S
Microwave study of quantum n-disk scattering Journal Article

(Abstract | Tags: Quantum Chaos)

Physical Review E, 61 (4), pp. 3652, 2000.
Pance, Kristi; Viola, Lorenza; Sridhar, S
Tunneling proximity resonances: interplay between symmetry and dissipation Journal Article

(Abstract | Tags: Quantum Chaos)

Physics Letters A, 268 (4-6), pp. 399–405, 2000.
Lu, Wentao; Viola, Lorenza; Pance, Kristi; Rose, Michael; Sridhar, S
Erratum: Microwave study of quantum n-disk scattering [Phys. Rev. E 61, 3652 (2000)] Journal Article

(Abstract | Tags: Quantum Chaos)

Physical Review E, 62 (3), pp. 4478, 2000.
Lu, Wentao; Rose, M; Pance, K; Sridhar, S
Quantum resonances and decay of a chaotic fractal repeller observed using microwaves Journal Article

(Abstract | Tags: Quantum Chaos)

Physical review letters, 82 (26), pp. 5233, 1999.
Sridhar, S
Wave Chaos and Localization in Closed Billiards and Open Scattering Systems: Microwave Experiments Inproceedings

(Abstract | Tags: Quantum Chaos)

APS March Meeting Abstracts, 1998.
Kudrolli, A; Sridhar, S
Experiments on quantum chaos using microwave cavities: Results for the pseudo-integrable L-billiard Journal Article

(Abstract | Tags: Quantum Chaos)

Pramana, 48 (2), pp. 459–467, 1997.
Jacobs, T; Willemsen, Balam A; Sridhar, S
Quantitative analysis of nonlinear microwave surface impedance from non-Lorentzian resonances of high Q resonators Journal Article

(Tags: Quantum Chaos)

Review of scientific instruments, 67 (10), pp. 3757–3758, 1996.
Kudrolli, A; Sridhar, S
Comment on “Gaussian Orthogonal Ensemble Statistics in a Microwave Stadium Billiard with Chaotic Dynamics: Porter-Thomas Distribution and Algebraic Decay of Time Correlations” Journal Article

(Abstract | Tags: Quantum Chaos)

Physical review letters, 76 (16), pp. 3036, 1996.
Kudrolli, A; Kidambi, V; Sridhar, S
Experimental studies of chaos and localization in quantum wave functions Journal Article

(Abstract | Tags: Quantum Chaos)

Physical review letters, 75 (5), pp. 822, 1995.
Prigodin, VN; Taniguchi, Nobuhiko; Kudrolli, A; Kidambi, V; Sridhar, S
Spatial correlation in quantum chaotic systems with time-reversal symmetry: Theory and experiment Journal Article

(Abstract | Tags: Quantum Chaos)

Physical review letters, 75 (12), pp. 2392, 1995.
Kudrolli, A; Sridhar, S
QUANTUM CHAOS EXPERIMENTS USING MICROWAVE CAVITIES Inproceedings

(Abstract | Tags: Quantum Chaos)

Proceedings Of The 2nd Experimental Chaos Conference, pp. 184, World Scientific 1995.
Sridhar, S
Cavities of Chaos Journal Article

(Tags: Quantum Chaos)

SCIENCE NEWS-WASHINGTON-, 147 , pp. 264–264, 1995.
Kudrolli, A; Sridhar, S; Pandey, Akhilesh; Ramaswamy, Ramakrishna
Signatures of chaos in quantum billiards: Microwave experiments Journal Article

(Abstract | Tags: Quantum Chaos)

Physical Review E, 49 (1), pp. R11, 1994.
Sridhar, S
Quantum Dynamics of Chaotic Systems Journal Article

(Tags: Quantum Chaos)

1993.
Sridhar, S; Hogenboom, D; Kudrolli, A
Exper-imental eigenvalue spectra of “rough” and multiplyconnected billiards,” Journal Article

(Abstract | Tags: Quantum Chaos)

Quantum Dynamics of Chaotic Systems, eds. Yuan, JM, Feng, DH & Zaslavsky, GM (Gordon and Breach, Amsterdam), pp. 297–304, 1993.
Sridhar, S; Heller, EJ
Physical and numerical experiments on the wave mechanics of classically chaotic systems Journal Article

(Abstract | Tags: Quantum Chaos)

Physical Review A, 46 (4), pp. R1728, 1992.
Sridhar, S; Hogenboom, DO; Willemsen, Balam A
Microwave experiments on chaotic billiards Journal Article

(Abstract | Tags: Quantum Chaos)

Journal of statistical physics, 68 (1-2), pp. 239–258, 1992.
Sridhar, S; Parimi, PV; Lu, WT; Vodo, P; Derov, John S; Hanscom, AFRL; Bedford, MA
Negative Refraction and Imaging in Photonic Crystals Journal Article

(Abstract | Tags: Quantum Chaos)

0000.
Harika, K; Swetha, BV; Renuka, B; Rao, Lakshman D; Sridhar, S
Analysis of Different Multiplication Algorithms & FPGA Implementation Journal Article

(Tags: Quantum Chaos)

IOSR Journal of VLSI and Signal Processing (IOSR-JVSP), 4 (2), pp. 29–35, 0000.